The third-ranked Russian, looking for her third title in Qatar, will play either Serena Williams or Petra Kvitova. If Williams reaches the semifinal, the 31-year-old American will be the oldest woman to reach No. 1.

Chris Evert held the top ranking in 1985 just shy of her 31st birthday.

Sharapova broke Stosur twice to lead 4-1 and hit a backhand down the line to make it 5-1. She closed it out when the ninth-ranked Australian hit her return long.

Sharapova took a 3-0 lead in the second set, but Stosur staged a brief comeback. Stosur broke to make it 3-1 and had a chance to tie it at 4-4. But Sharapova hit five aces to win the game and won the set when her backhand clipped the net and dropped over.

"I was happy because Sam certainly stepped up her level in the second set," Sharapova said. "I really started playing well when I had to and being aggressive at the right times."

Sharapova has an outside chance of returning to No. 1 for the sixth time. But Williams and top-ranked Azarenka would have to lose.

If Williams loses to Kvitova, Azarenka would retain the top spot by reaching the final. Sharapova would return to No. 1 if the other two falter and she wins the tournament.

"Is it great to have the opportunity to come back to that position? I mean, we'd be lying if we weren't. We're excited about having the chance," she said. "The ranking is always one of those things where it also depends on the other players' success and the amount of points and the tournaments that they play.

"That's out of my control, so that's the reason why, to me, maybe it's not as important as winning the match point of a Grand Slam. Whereas, you wake up on a Monday morning and the ranking system changed and you're No. 1 in the world."